Finite Group Databasebeta

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C9×C13×Dic23 #24924470

order10764
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×Dic23
unambiguous semidirect productC23⋊(C4×C9×C13)

Splittings

derived, SylowC23 ⋊ C4×C9×C13
HallC9×C13×C23 ⋊ C4
HallC13×C23 ⋊ C4×C9
HallC9×C23 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C13D23
commutator, hypocenterC23C4×C9×C13
FrattiniC2×C3C3×C13×D23
FittingC2×C9×C13×C23C2
socle, prime radicalC2×C3×C13×C23C2×C3
cosocleC2×C3×C23C2×C3×C13
LCSG ▷ C23
UCSC1 ◁ C2×C9×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 6);